Smith hit a dashing 95 in just his fourth innings at the top level as the hosts flipped their fortunes from 54-5 to 376 all out on day two of the third Test.
Chris Woakes and Gus Atkinson then plunged the tourists into further peril, striking with the new ball as the West Indies closed on 33-2 trailing by 61.
Joe Root had started the fightback with a controlled 87, passing 12,000 Test runs and leapfrogging Caribbean great Brian Lara along the way, but it was Smith's verve that carried England into an eventual lead of 94.
The 24-year-old, picked ahead of Jonny Bairstow and Ben Foakes for this series in a changing-of-the-guard moment, bristled with attacking intent as he showed off the flair that inspired the selectors to make the switch.
There were 12 fours in his 109-ball stay as he worked through his range of shots but he will remember the innings best for an audacious six that cleared the Eric Hollies Stand. He had only been at the crease a few minutes when he launched a pull high over the rowdiest crowd in the country and, for the second time in three games, the stadium was not big enough to contain him.
On the balcony Ben Stokes's eyes were on stalks as he watched the ball sail over the roof, the England skipper visibly excited by the power of his newest recruit.
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